Probability Questions and Solved Examples
Here is the giant combined cheat sheet with all questions, tables, charts, calculations, and answers included. You can copy this into a document editor and save it as a PDF.
Probability Questions and Answers
Question 1
Statement: Tossing a coin and getting a head, and then rolling a 6-sided die and getting a 5. Are these events dependent?
Answer: False
Explanation: The events are independent because the outcome of the coin toss does not affect the die roll.
Question 2
Which pairs of events are disjoint?
Read MoreStatistics Problems and Solutions
1. Blood Cholesterol Analysis
Blood cholesterol was measured on a random sample of 24 people:
226, 189, 240, 192, 216, 207, 221, 255, 190, 237, 219, 182, 209, 198, 243, 202, 234, 194, 213, 185, 193, 223, 204, 191
i) Stem-and-Leaf Plots
The first 18 observations have been entered in the stem-and-leaf plot on the left. The completed plot is shown on the right.
Left Plot (Original Entries in Bold) | Right Plot (Ordered)
25 | 5 | 25 | 5
24 | 0 3 | 24 | 0 3
23 | 7 4 | 23 | 4 7
22 | 6 1 3 | 22 | 1 3 6
21 | 6 9
Read MoreResearch Methods: A Comprehensive Study
Side 1: Chapter 4 – Research Design
Definition
The plan or blueprint for a study, outlining how data will be collected and analyzed.
Types
- Exploratory
- Descriptive
- Causal
Key Research Design Types
Exploratory Research
Conducted when little is known, aims to gain insights and clarify ideas.
Descriptive Research
Provides a detailed description of phenomena, without manipulation.
Causal Research
Establishes cause-and-effect relationships between variables.
Sampling Design
Probability Sampling
Every member of the population
Read MoreKey Concepts in Statistics: Data, Methods & Limitations
Limitations of Statistics
-
Statistics does not deal with individuals:
- Statistics deals with an aggregate of facts and does not give specific recognition to individual items in a series.
- It deals with groups of individuals and indicates the characteristics of the whole group.
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Statistics does not deal directly with qualitative characteristics:
- Statistical methods can only be applied to numerically expressed data.
- A qualitative phenomenon must be converted into quantitative information before statistical
Understanding Statistical Variability and Distributions
Understanding Measures of Variability
Measures of variability indicate how much scores in a distribution vary, either from the mean or across the full extent of the distribution. It represents the spread of all the scores. Four measures of variability are discussed here: the range, the average mean deviation, the variance, and the standard deviation. These measures can reveal the consistency or similarity of the scores in a distribution and the extent to which the mean truly represents all of the
Read MoreUnderstanding Disease Frequency: Incidence, Prevalence, and Public Health Measures
Definition of Proportion
- A measure that states a count relative to the size of the group.
- A ratio in which the numerator is part of the denominator.
- May be expressed as a percentage.
Definition of Rate
- A ratio that consists of a numerator and a denominator and in which time forms part of the denominator.
- Contains the following elements:
- Disease frequency
- Unit size of population
- Time period during which an event occurs
Example of Rate Calculation
Definition of Prevalence
The number of existing cases of a disease
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